Earlier on Tuesday the youth wing of Zimbabwe's ruling party accused Chiwenga of subverting the constitution for threatening military intervention.
Last week, he sacked Mnangagwa, a former defense minister with strong ties to the military, replacing him with Mugabe's wife Grace, 52.
This photo taken November 8, 2017, shows Zimbabwe's President Robert Mugabe, left, addressing party members and supporters to show support to Grace Mugabe, right, becoming the party's next vice president after the dismissal of Emerson Mnangagwa.
Chiwenga, a political ally of Mnangagwa, added that the Zanu-PF had been hijacked by people who did not fight in the 1970s liberation war, which some commentators read as a criticism of Ms Mugabe, a vocal critic of the former vice president.
In a statement, the party spokesman said Chiwenga's stance was "clearly calculated to disturb national peace... and suggests treasonable conduct on his part as this was meant to incite insurrection".
"(Mugabe) has previously warned the military to stay away from ZANU-PF's succession race. Whilst reports on social media seem to imply that a coup is underway, Khuluma Afrika understands that military presence has been increased there to improve security in the face of growing uncertainty in the country. Four army tanks were seen heading toward the Zimbabwean capital Harare on Tuesday, witnesses said.
The ruling party will next month hold an extra ordinary congress to reaffirm Mugabe's candidature in next year's presidential elections and also amend the party constitution to allow for a female vice president.
Images posted on Twitter showed tanks and trucks loaded with troops, reportedly traveling along the road toward the capital Harare.
"We must remind those behind the current treacherous shenanigans that, when it comes to matters of protecting our revolution, the military will not hesitate to step in", said General Constantino Chiwenga in a statement.
Earlier this year the country was gripped by a freaky spat between Grace and Mnangagwa that included an alleged ice-cream poisoning incident that laid bare the pair's rivalry.
"As a result of squabbling within the ranks of Zanu-PF, there has been no meaningful development in the country for the past five years".
President Robert Mugabe with his wife Grace Mugabe.
"Chiwenga threw down the gauntlet to Mugabe.it would make sense for Chiwenga to organise some military manoeuvres to up the ante".
"The current purging ... targeting members of the party with a liberation background must stop forthwith", he said.
Grace Mugabe - 41 years younger than her husband - has become increasingly active in public life in what many say is a process to help her eventually take the top job.